\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
=\(\frac{1}{3}.\left(\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{1}{30.33}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{30}-\frac{1}{33}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\)
=\(\frac{1}{3}.\frac{10}{33}\)
=\(\frac{10}{99}\)
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